Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles... SYLLABUS OF PLANE GEOMETRY - Side 171876Uten tilgangsbegrensning - Om denne boken
| William Frothingham Bradbury - 1872 - 110 sider
...DEH are equiangular (I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 Two triangles having **an angle of the one equal to an angle of the other,** and the sides including these angles proportional, are similar. In the triangles ABC,DEF let tiifl... | |
| David Munn - 1873
...opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. Two triangles which have **an angle of the one equal to an angle of the other,** are to each other as the products of the sides including the equal angles 47 IX. The areas of similar... | |
| Benjamin Greenleaf - 1873 - 176 sider
...the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have **an angle of the one equal to an angle of the other,** and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have... | |
| Euclides - 1874
...equal PKOP. XI— THEOREM. (Euc. VI. 14, 15.) Equal parallelograms and equal triangles, which have **an angle of the one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional; and conversely. Let MB and BN be... | |
| L J V. Gerard - 1874
...are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have **an angle of the one equal to an angle of the other,** have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
| Benjamin Greenleaf - 1874 - 176 sider
...the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have **an angle of the one equal to an angle of the other,** and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have... | |
| Euclides - 1874
...intercepted area, according as they intersect internally or externally. 15. If two trapeziums have **an angle of the one equal to an angle of the other,** and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Aaron Schuyler - 1876 - 364 sider
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having **an angle of the one equal to an angle of the other,** and tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB :... | |
| Richard Wormell - 1876
...demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and have **an angle of the one equal to an angle of the other,** then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
| 1876
...polygons. Prove that two triangles are similar when they are mutually equiangular. 2. Two triangles having **an angle of the one equal to an angle of the other** are to each other as the products of the sides including the equal angles. 3. To inscribe A circle... | |
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